Difference between revisions of "Superstructure"
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(Created page with "<font color="blue">Surstructure </font> (''Fr''). <font color="black">Superstruttura </font> (''It''). <font color="purple">超構造 </font> (''Ja''). A '''superstructure''' i...") |
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A '''superstructure''' is a [[crystal structure]] S’ obtained from another crystal structure (called a '''basic structure''') S under the following conditions: | A '''superstructure''' is a [[crystal structure]] S’ obtained from another crystal structure (called a '''basic structure''') S under the following conditions: | ||
*the space group G’ of S is a subgroup of the space group G of S; | *the space group G’ of S is a subgroup of the space group G of S; | ||
| − | *the translation subgroup T(G’) of S’ is a subgroup of translation subgroup T(G) of S, i.e. the [[unit cell]] of S’ is a supercell of the unit cell of S and the [[lattice]] of S’ is [[sublattice]] of the lattice of S; | + | *the translation subgroup T(G’) of S’ is a subgroup of translation subgroup T(G) of S, ''i.e.'' the [[unit cell]] of S’ is a supercell of the unit cell of S and the [[lattice]] of S’ is [[sublattice]] of the lattice of S; |
*the point group of P’ of S’ may either coincide with the point group P of S or be a subgroup of it; | *the point group of P’ of S’ may either coincide with the point group P of S or be a subgroup of it; | ||
*at least one of the [[Wyckoff position]]s of S is split into two or more independent Wyckoff positions of S’ and the corresponding [[crystallographic orbit]]s are occupied by chemically different atoms. | *at least one of the [[Wyckoff position]]s of S is split into two or more independent Wyckoff positions of S’ and the corresponding [[crystallographic orbit]]s are occupied by chemically different atoms. | ||
| − | [[Image:basic structure.png|right|thumb|A structure S composed | + | [[Image:basic structure.png|right|thumb|A structure S composed of a single crystallographic orbit]] |
[[Image:superstructure.png|right|thumb|A structure S' obtained from S by reducing its translational symmetry. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a '''basic structure''', S' a '''superstructure''' of S. Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the ''b'' direction that are lost in the superstructure.]] | [[Image:superstructure.png|right|thumb|A structure S' obtained from S by reducing its translational symmetry. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a '''basic structure''', S' a '''superstructure''' of S. Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the ''b'' direction that are lost in the superstructure.]] | ||
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*[[Derivative structure]] | *[[Derivative structure]] | ||
*[[Substructure]] | *[[Substructure]] | ||
| − | *Martin J. | + | *Buerger, Martin J. (1947). ''J. Chem. Phys.'' '''15''', 1-16. |
| + | |||
| + | [[Category:Crystal chemistry]] | ||
| + | [[Category:Fundamental crystallography]] | ||
Latest revision as of 13:34, 15 July 2021
Surstructure (Fr). Superstruttura (It). 超構造 (Ja).
A superstructure is a crystal structure S’ obtained from another crystal structure (called a basic structure) S under the following conditions:
- the space group G’ of S is a subgroup of the space group G of S;
- the translation subgroup T(G’) of S’ is a subgroup of translation subgroup T(G) of S, i.e. the unit cell of S’ is a supercell of the unit cell of S and the lattice of S’ is sublattice of the lattice of S;
- the point group of P’ of S’ may either coincide with the point group P of S or be a subgroup of it;
- at least one of the Wyckoff positions of S is split into two or more independent Wyckoff positions of S’ and the corresponding crystallographic orbits are occupied by chemically different atoms.
A structure S' obtained from S by reducing its translational symmetry. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a basic structure, S' a superstructure of S. Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the b direction that are lost in the superstructure.
See also
- Derivative structure
- Substructure
- Buerger, Martin J. (1947). J. Chem. Phys. 15, 1-16.